On iterated powers of positive definite functions

We prove that if $\rho$ is an adapted positive definite function in the Fourier--Stieltjes algebra $B(G)$ of a locally compact group $G$ with $\|\rho\|_{B(G)}=1$, then the iterated powers $(\rho^n)$ converge to zero in the weak* topology $\sigma(B(G) , C^*(G))$. Moreover, if $\rho$ is irreducible, we prove that $(\rho^n)$ as a sequence of u.c.p. maps on the group $C^*$-algebra converges to zero in the strong operator topology

The three-nucleon system as a laboratory for nuclear physics: the need for 3N forces

Recent experimental results in three-body systems have unambiguously shown that calculations based on nucleon-nucleon forces fail to accurately describe many experimental observables and one needs to include effects which are beyond the realm of the two-body potentials. This conclusion owes its significance to the fact that experiments and calculations can both be performed with a high accuracy. In this short review, a sample of recent experimental results along with the results of the state-of-the-art calculations will be presented and discussed.Comment: Commissioned article for Nuclear Physics News, 8 pages, 6 figure